Question

given an odd integer a,establish that a^2 + (a+4)^2 +1 is divisible by 12​

Answer 1

Step-by-step explanation:

a²+(a+2)²+(a+4)²+2

a²+a²+4a+4+a²+8a+16+1

3a²+12a+21

3(a²+4a+7)

Since a is odd a=2k+1

3((2k+1)²+4(2k+1)+7)

3(4k²+4k+1+8k+4+7)

3(4k²+12k+12)

3(4)(k²+3k+3)

12(k²+3k+3)

It is divisible by 12.